That 10 essentials list is pretty good to get an idea to start with, other than the axe, I don't think you really need one in Florida. The truth is, your gear will evolve with experience as you find out what works for you, it's inevitable no matter what you start out with.
Also, in my opinion, you don't need a huge medical kit. Mine has 2 tear open packets of neosporin, some gauze, a couple painkillers, a band aid or two and a compression wrap type thing. I'd say the most important thing is the neosporin. Don't get loaded down with a bunch of medical equipment that you really can't use (unless you're an emt or something but then I'm sure you know better than me anyway.)